Step 1: Construct the base square: Fill the magic square with 1-5, so that the two diagonal lines are 12345 and 33333 respectively, and the sum of each row and column is 15, as shown below.
1 4 2 5 3
4 2 5 3 1
2 5 3 1 4
5 3 1 4 2
3 1 4 2 5
Step 2: Then construct the square root: turn the base square around, subtract 1 from each number, and multiply it by 5 to get the following results.
10 20 5 15 0
0 10 20 5 15
15 0 10 20 5
5 15 0 10 20
20 5 15 0 10
Step 3: Add the numbers in each corresponding cell of the root and the bottom to get the final magic square.
1 1 24 7 20 3
4 12 25 8 16
17 5 13 2 1 9
10 18 1 14 22
23 6 19 2 15
That's 25 squares.
evolutionary process
On the river map, black spots and white spots arranged in several arrays contain infinite mysteries; The pattern on Luoshu just corresponds to nine numbers from 1 to 9, and the sum of three numbers on vertical, horizontal, oblique and three lines is equal to 15. At that time, people didn't know it was the third-order magic square in modern mathematics. They called this mysterious arrangement of numbers Nine palace map.
Scholars at home and abroad have conducted long-term exploration and research on this issue, believing that it is the crystallization of the spiritual thinking of Chinese ancestors and the first milestone of ancient civilization in China.